ELE2120 Digital Circuits and Systems

Tutorial Note 7

Outline

1. Sequential Circuit

2. Gated SR Latch

4. Edge-Triggered D Flip-Flop

3. Gated D-latch

5. Asynchronous and Synchronous reset

Sequential Circuit

The sequential circuits: circuits whose output depends upon both the input of

the circuit and its previous state. In other words, they are circuits that have

memory.

For a device to serve as a memory, it must have three characteristics:

1. the device must have two stable states.

2. there must be a way to read the state of the device.

3. there must be a way to set the state at least once.

One can remove the input that caused a particular

output and the output will be unchanged!

Examples for Sequential Circuit

(a2) Gated SR Latch (AND)

Gated SR Latch

(a1) Gated SR Latch (NAND)

CLK S R Q(t+1)

0 X X Q(t)(Retain)

1 0 0 Q(t)(Retain)

1 0 1 0

1 1 0 1

1 1 1 X

(c) Characteristics table

(b) Graphical Symbol

(d) Timing Diagram

Gated SR Latch

(a2) Gated SR Latch (AND) (a1) Gated SR Latch (NAND)

1. (a1) CLK is gated by NAND gates.

2. S & R inputs are reversed.

3. Fewer transistors than AND gates.

4. Gated SR Latches with NAND: standard.

Question: What is the transistors number for (a1) and (a2)?

(a1): 4*2-input-NAND=4*(2n)=4*(2*2)=16

(a2): 2*2-input-AND+2*2-input-NOR=2*(2n+2)+2*(2n)=2*6+2*4=20

(b) Graphical Symbol

Gated SR Latch Exercise

Exercise:

Let the SR input waveforms be in figure 1. Show the Q output

waveform for the SR latches using NAND and NOR gates.

(Assume present state of Q is 0)

Figure1

CLK

S

R

Q

Gated D-Latch

CLK D Q(t+1)

0 X Q(t)

1 0 0

1 1 1

(a) Gated D Latch (NAND)

(c) Characteristics table

(b) Graphical Symbol

(d) Timing Diagram

Effect of Propagation Delay

Typical values for CMOS technology:

tsu = tsetup = 3 ns

th = thold = 2 ns

The addition transistor in CMOS(in contrast to other forms of MOS logic, has both

NMOS and PMOS) not only increases the chip area but also increases the total

effective capacitance per gate and in turn increases the propagation delay

(a).Propagation Delay

Effect of Propagation Delay

The flip-flop is a leading edge triggered D-type. Data on the input signal D is clocked into the flip-flop on the leading edge of the

clock signal. This data then appears on the output terminal Q of the flip-flop.

In order to ensure correct operation of the flip-flop, the input data Din must be stable and valid for a duration tsetup, before the

clock signal reaches the input voltage threshold of the flip-flop. It must then remain at this value for a duration thold, after the clock

signal has reached input threshold voltage. After the time thold has elapsed the input data Din can be changed without changing

the state of the flip-flop.

Master-Slave D flip-flop

(b) Graphical Symbol (a) Master-Slave D flip-flop

(c) Timing Diagram

Flip-flop denotes a storage element that changes its output state

at the edge of a controlling clock signal

Edge-Triggered D Flip-Flop

(a) Edge-Triggered D Flip-Flop

(b) Graphical Symbol

Clock = 0 P1 = P2 = 1

Retain Q,Q’ state

P3=D, P4=D’

Clock = 1

Q=D

Q’=D’

P1=D’

P2=D

Asynchronous Reset for a D Flip-Flop

(a) Master-Slave D flip-flop with Clear and Present

Master Slave (b) Graphical Symbol

CLK D Pres Clear Q

x x 0 0 (----)

x x 1 0 0

x x 0 1 1

0 1 1 0

1 1 1 1

0,1, X 1 1 Q(retain)

Flip-flop goes into the state Q=0 immediately.

Asynchronous clear!

Synchronous Reset for a D Flip-Flop

For Synchronous Reset for D Flip-flop, when Clear goes

to 1, then on the next positive edge of the clock the

flip‐flop will be cleared to 0.

For Asynchronous Reset for D Flip-flop, when Clear

goes to 0, then on the flip‐flop will be cleared to 0

immediately.

(b) D flip-flop with Preset and Clear

(a) D flip-flop with synchronous clear

T(Toggle) flip-flop

(b) Graphical symbol

T Q(t+1)

0 Q(t)

1 Q(t)’

(c) Truth Table(d) Time DiagramNo Change to Output

Complement the Output

T flip-flop Exercise 1

Exercise1:

How can I decrease the frequency of the clock signal to 1/8 of its original

by using 3 T flip-flop? (Consider initial Q = 1)

Character of T Flip-flop

1 CLK

½ CLK

½ CLK

1 CLK

1/4 CLK

1/2 CLK

1/8 CLK

JK flip-flop

J K Q(t+1)

0 0 Q(t)

0 1 0

1 0 1

1 1 Q(t)’

(b) Graphical symbol

(a) JK flip-flop Circuit

(c) Truth Table

JK flip-flop combines the behaviors of SR and T flip-flops in a useful way. •When J=S, K=R, for all input values except J=K=1 it behaves as the SR flip-flop•When J and K connected together, it can also serve as a T flip-flop.

Characteristic Equation

Specify next state as a function of its current state and inputs

• Q(t) current state

• Q(t+1) next state

For example:

• SR latch: Q(t+1) = S + R’Q(t)

• D flip-flop: Q(t+1) = D

• JK flip-flop: Q(t+1) = JQ’(t)+K’Q(t)

• T flip-flop: Q(t+1) = T⊕Q(t)= TQ’(t)+T’Q(t)